Question 1

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

Accepted Answer

A)  in stable equilibrium 
B)  in unstable equilibrium 
C)  in neutral equilibrium 
D)  not in equilibrium 
E)  none of the above 
A)  in stable equilibrium 
B)  in unstable equilibrium 
C)  in neutral equilibrium 
D)  not in equilibrium 
E)  none of the above

Question 2

Two supports, made of the same material and initially of equal length, are 2.0 m apart. A stiff board with a length of 4.0 m and a mass of 10 kg is placed on the supports, with one support at the left end and the other at the midpoint. A block is placed on the board a distance of 0.50 m from left end. As a result the board is horizontal (that is, the downward force on each support is the same). The mass of the block is:

Accepted Answer

A)  0 kg 
B)  2.3 kg 
C)  6.6 kg 
D)  10 kg 
E)  20 kg 
A)  0 kg 
B)  2.3 kg 
C)  6.6 kg 
D)  10 kg 
E)  20 kg

Question 3

A horizontal beam of weight W is supported by a hinge and cable as shown. The force exerted on the beam by the hinge has a vertical component that must be:

Accepted Answer

A)  nonzero and up 
B)  nonzero and down 
C)  nonzero but not enough information given to know whether up or down 
D)  zero 
E)  equal to W 
A)  nonzero and up 
B)  nonzero and down 
C)  nonzero but not enough information given to know whether up or down 
D)  zero 
E)  equal to W

Question 4

A picture can be hung on a wall in three different ways, as shown. The tension in the string is:

Accepted Answer

A)  least in I 
B)  greatest in I 
C)  greatest in II 
D)  least in III 
E)  greatest in III 
A)  least in I 
B)  greatest in I 
C)  greatest in II 
D)  least in III 
E)  greatest in III

Question 5

A uniform ladder is 10 m long and weighs 400 N. It rests with its upper end against a frictionless vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground. The ladder makes a 30 $\degree$ angle with the horizontal. The force exerted on the wall by the ladder is:

Accepted Answer

A)  47 N 
B)  74 N 
C)  120 N 
D)  350 N 
E)  460 N 
A)  47 N 
B)  74 N 
C)  120 N 
D)  350 N 
E)  460 N

Question 6

A picture is to be hung from the ceiling by means of two wires. Order the following arrangements of the wires according to the tension in wire B, from least to greatest.

Accepted Answer

A)  I, II, III 
B)  III, I, II 
C)  I and II tie, then III 
D)  II, I, III 
E)  all tie 
A)  I, II, III 
B)  III, I, II 
C)  I and II tie, then III 
D)  II, I, III 
E)  all tie

Question 7

A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 * 109 N/m2. When it is subjected to a pressure of 3.0*105 Pa its volume is:

Accepted Answer

A)  7.31 cm3 
B)  7.99931 cm3 
C)  8.00069 cm3 
D)  8.69 cm3 
E)  none of these 
A)  7.31 cm3 
B)  7.99931 cm3 
C)  8.00069 cm3 
D)  8.69 cm3 
E)  none of these

Question 8

A window washer attempts to lean a ladder against a frictionless wall. He finds that the ladder slips on the ground when it is placed at an angle of less than 75 $\degree$ to the ground but remains in place when the angle is greater than 75 $\degree$. The coefficient of static friction between the ladder and the ground:

Accepted Answer

A)  is 0.13 
B)  is 0.27 
C)  is 1.3 
D)  depends on the mass of the ladder 
E)  depends on the length of the ladder 
A)  is 0.13 
B)  is 0.27 
C)  is 1.3 
D)  depends on the mass of the ladder 
E)  depends on the length of the ladder

Question 9

The pull P is just sufficient to keep the 14-N block and the weightless pulleys in equilibrium as shown. The tension T in the upper cable is:

Accepted Answer

A)  14 N 
B)  28 N 
C)  16 N 
D)  9.3 N 
E)  19 N 
A)  14 N 
B)  28 N 
C)  16 N 
D)  9.3 N 
E)  19 N

Question 10

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm. Assuming g is constant, what is the location of the center of mass xcom, and the location of the center of gravity xcog, of the two masses?

Accepted Answer

A)  xcom = 1.5 cm, xcog = 3.4 cm 
B)  xcom = 3.4 cm, xcog = 1.5 cm 
C)  xcom = 1.5 cm, xcog = 1.5 cm 
D)  xcom = 3.4 cm, xcog = 3.4 cm 
E)  xcom = 1.5 cm, xcog = 0 cm 
A)  xcom = 1.5 cm, xcog = 3.4 cm 
B)  xcom = 3.4 cm, xcog = 1.5 cm 
C)  xcom = 1.5 cm, xcog = 1.5 cm 
D)  xcom = 3.4 cm, xcog = 3.4 cm 
E)  xcom = 1.5 cm, xcog = 0 cm

Question 11

The bulk modulus is a proportionality constant that relates the pressure acting on an object to:

Accepted Answer

A)  the shear 
B)  the fractional change in volume 
C)  the fractional change in length 
D)  Young's modulus 
E)  the spring constant 
A)  the shear 
B)  the fractional change in volume 
C)  the fractional change in length 
D)  Young's modulus 
E)  the spring constant

Question 12

If you sit on an ordinary 4-legged chair, which of the following is true?

Accepted Answer

A)  As long as you know your weight and the point at which it acts on the chair, you can calculate the forces exerted by all four chair legs on the floor. 
B)  As long as you know your weight and the point at which it acts on the chair, you can calculate the forces exerted by all four chair legs on the floor, but only if your own feet are not also on the floor. 
C)  This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated. 
D)  This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated without knowing how your weight is distributed on the chair. 
E)  This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated without knowing how the chair deforms due to your weight. 
A)  As long as you know your weight and the point at which it acts on the chair, you can calculate the forces exerted by all four chair legs on the floor. 
B)  As long as you know your weight and the point at which it acts on the chair, you can calculate the forces exerted by all four chair legs on the floor, but only if your own feet are not also on the floor. 
C)  This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated. 
D)  This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated without knowing how your weight is distributed on the chair. 
E)  This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated without knowing how the chair deforms due to your weight.

Question 13

To shear a cube-shaped object, forces of equal magnitude and opposite directions might be applied:

Accepted Answer

A)  to opposite faces, perpendicular to the faces 
B)  to opposite faces, parallel to the faces 
C)  to adjacent faces, perpendicular to the faces 
D)  to adjacent faces, neither parallel nor perpendicular to the faces 
E)  to a single face, in any direction 
A)  to opposite faces, perpendicular to the faces 
B)  to opposite faces, parallel to the faces 
C)  to adjacent faces, perpendicular to the faces 
D)  to adjacent faces, neither parallel nor perpendicular to the faces 
E)  to a single face, in any direction

Question 14

A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7* 105 N/m2. When it is subjected to a pressure of 2.0 * 105 Pa the length in cm of its any of its any of its sides is:

Accepted Answer

A)  0.85 cm 
B)  1.15 cm 
C)  1.66 cm 
D)  2.0 cm 
E)  none of these 
A)  0.85 cm 
B)  1.15 cm 
C)  1.66 cm 
D)  2.0 cm 
E)  none of these

Question 15

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:

Accepted Answer

A)  the center of mass 
B)  the center of gravity 
C)  the geometrical center 
D)  the point of application of the force 
E)  the same point 
A)  the center of mass 
B)  the center of gravity 
C)  the geometrical center 
D)  the point of application of the force 
E)  the same point

Question 16

A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 mm and a Young's modulus of 125* 108 N/m2. The elongation of the rod is:

Accepted Answer

A)  0.022 mm 
B)  0.0040 mm 
C)  0.11 mm 
D)  0.55 mm 
E)  1.42 mm 
A)  0.022 mm 
B)  0.0040 mm 
C)  0.11 mm 
D)  0.55 mm 
E)  1.42 mm

Question 17

An 80-N uniform plank leans against a frictionless wall as shown. The torque (about point P) applied to the plank by the wall is:

Accepted Answer

A)  40 N.m 
B)  60 N.m 
C)  120 N.m 
D)  160 N.m 
E)  240 N.m 
A)  40 N.m 
B)  60 N.m 
C)  120 N.m 
D)  160 N.m 
E)  240 N.m

Exam 12: Equilibrium and Elasticity

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

A horizontal beam of weight W is supported by a hinge and cable as shown. The force exerted on the beam by the hinge has a vertical component that must be:

A picture can be hung on a wall in three different ways, as shown. The tension in the string is:

A picture is to be hung from the ceiling by means of two wires. Order the following arrangements of the wires according to the tension in wire B, from least to greatest.

A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 * 109 N/m2. When it is subjected to a pressure of 3.0*105 Pa its volume is:

The pull P is just sufficient to keep the 14-N block and the weightless pulleys in equilibrium as shown. The tension T in the upper cable is:

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm. Assuming g is constant, what is the location of the center of mass xcom, and the location of the center of gravity xcog, of the two masses?

The bulk modulus is a proportionality constant that relates the pressure acting on an object to:

If you sit on an ordinary 4-legged chair, which of the following is true?

To shear a cube-shaped object, forces of equal magnitude and opposite directions might be applied:

A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7* 105 N/m2. When it is subjected to a pressure of 2.0 * 105 Pa the length in cm of its any of its any of its sides is:

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:

A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 mm and a Young's modulus of 125* 108 N/m2. The elongation of the rod is:

An 80-N uniform plank leans against a frictionless wall as shown. The torque (about point P) applied to the plank by the wall is:

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A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 * 10⁹ N/m². When it is subjected to a pressure of 3.0*10⁵ Pa its volume is:

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm. Assuming g is constant, what is the location of the center of mass x_com, and the location of the center of gravity x_cog, of the two masses?

A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7* 10⁵ N/m². When it is subjected to a pressure of 2.0 * 10⁵ Pa the length in cm of its any of its any of its sides is:

A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 mm and a Young's modulus of 125* 10⁸ N/m². The elongation of the rod is: